Note on integral closures of semigroup rings (Q2724918)

The author gives conditions for the semigroup ring \(R[S]\) (relative to a commutative ring \(R\) and to a subsemigroup \(S\), containing \(0\), of a torsion free Abelian group) to be integrally closed. He proves that this property is reduced to consider the polynomial ring of an indeterminate over a reduced total quotient ring. Moreover, if the quotient ring of \(R\) satisfies that for all \(a\in R\) there exists \(b\in R\) such that \(a=a^2b\), then \(R[S]\) is integrally closed if, and only if, \(R\) and \(S\) are so.